Question

Analytic continuation of the function $f=\sqrt[3]{z^2-1}$

score 59 · Answer 1 · 2022-07-27 15:43:33

59

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Analytic continuation of the function $f=\sqrt[3]{z^2-1}$

Published on 27 Jul 2022 - 15:43

score 546 · Answer 2 · 2022-08-03 20:11:53

546

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Suppose $f$ is holomorphic on $\mathbb{C}\setminus\{0\}$ and $f(n)=(-1)^n$ for each positive integer $n$. Prove $\inf_{z\neq 0} |f(z)|=0$.

Published on 03 Aug 2022 - 20:11

score 122 · Answer 3 · 2022-08-21 18:42:36

122

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When will a Taylor series analytically continue a holomorphic function?

Published on 21 Aug 2022 - 18:42

score 47 · Answer 4 · 2022-08-30 15:42:05

47

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Basic question on specific case of analytic continuation

Published on 30 Aug 2022 - 15:42

score 66 · Answer 5 · 2026-03-27 22:53:03

66

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Question on convergence of product and Dirichlet series representations of a function

Published on 27 Mar 2026 - 22:53

score 82 · Answer 6 · 2026-02-24 07:11:46

82

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Inverse and extension of the $n$th Airy Ai and Bi zero

Published on 24 Feb 2026 - 7:11

score 120 · Answer 7 · 2022-09-14 12:25:06

120

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How does Mathematica compute certain "bad" cases of the Meijer G function?

Published on 14 Sep 2022 - 12:25

score 43 · Answer 8 · 2022-09-15 18:17:38

43

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A doubt regarding Cauchy's theorem and analytic continuation

Published on 15 Sep 2022 - 18:17

score 82 · Answer 9 · 2022-10-11 02:45:03

82

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Is analytic continuation the same as solving a PDE boundary problem with Cauchy Riemann

Published on 11 Oct 2022 - 2:45

score 117 · Answer 10 · 2026-03-25 17:40:32

117

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Doubt in application of monodromy theorem to Picard little theorem

Published on 25 Mar 2026 - 17:40

score 61 · Answer 11 · 2022-10-26 16:10:52

61

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analytic continuation of the spectral zeta function

Published on 26 Oct 2022 - 16:10

score 340 · Answer 12 · 2026-03-27 11:48:10

340

Views

Analytic continuation of the function $\sqrt{z^2 + 1}$ with the principal branch of the square root

Published on 27 Mar 2026 - 11:48

score 510 · Answer 13 · 2022-11-08 17:31:33

510

Views

Infinite series as integral representation

Published on 08 Nov 2022 - 17:31

score 54 · Answer 14 · 2022-11-09 06:35:22

54

Views

What is the qualitative relationship between an analytic function and its analytic continuation on the complement of the originally defined domain?

Published on 09 Nov 2022 - 6:35

score 37 · Answer 15 · 2022-11-15 13:31:39

37

Views

How can you prove that a function in z is Holomorphic(infinitely differentiable along all paths) through Cauchy Reimann conditions(proof: x, y only)

Published on 15 Nov 2022 - 13:31

List Question

Analytic continuation of the function $f=\sqrt[3]{z^2-1}$

Suppose $f$ is holomorphic on $\mathbb{C}\setminus\{0\}$ and $f(n)=(-1)^n$ for each positive integer $n$. Prove $\inf_{z\neq 0} |f(z)|=0$.

When will a Taylor series analytically continue a holomorphic function?

Basic question on specific case of analytic continuation

Question on convergence of product and Dirichlet series representations of a function

Inverse and extension of the $n$th Airy Ai and Bi zero

How does Mathematica compute certain "bad" cases of the Meijer G function?

A doubt regarding Cauchy's theorem and analytic continuation

Is analytic continuation the same as solving a PDE boundary problem with Cauchy Riemann

Doubt in application of monodromy theorem to Picard little theorem

analytic continuation of the spectral zeta function

Analytic continuation of the function $\sqrt{z^2 + 1}$ with the principal branch of the square root

Infinite series as integral representation

What is the qualitative relationship between an analytic function and its analytic continuation on the complement of the originally defined domain?

How can you prove that a function in z is Holomorphic(infinitely differentiable along all paths) through Cauchy Reimann conditions(proof: x, y only)

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